Abstract:
Rotor neurons are introduced to encode states living on the
surface of a sphere in D dimensions. Such rotors can
be regarded as continuous generalizations of binary (Ising)
neurons. The corresponding mean field equations are derived,
and phase transition properties based on linearized dynamics
are given. The power of this approach is illustrated with an
optimization problem -- placing N identical charges on
a sphere such that the overall repulsive energy is minimized.
The rotor approach appears superior to other methods for this
problem both with respect to solution quality and
computational effort needed.